Steve and Nickie are at the library. They are reading the same book for a class. They make a bet to see who is the farthest along after 1 hour of reading. The winner decides what to eat for lunch. After an hour, Steve says he has read

of the book. Nickie says she has read 65% of the book. Who will get to decide what to eat for lunch?In this concept, you will learn to compare and order fractions, decimals, and percents.

### Comparing Fractions, Decimals, and Percents

You can compare fractions, decimals and percents using greater than, less than or equal to. Convert fractions, decimals, and percents to the same form to compare the values. If you are comparing a fraction and a percent, write both of them either as fractions or percents to figure out which is greater. Use this information to write a set of numbers or quantities in order from least to greatest or from greatest to least.

Compare 45% and

.First, write 45% and \begin{align*}\frac{4}{5}\end{align*} to a percent. Find the equivalent fraction of as a fraction out of 100. Multiply both numerator and denominator by 20.

in the same form. Let’s change

Next, convert the fraction to a percent.

Now, we can compare 45% and 80%.

45% is less than 80%.

Let’s compare percents and decimals.

Compare 18% and 0.9.

First, write 18% and 0.9 in the same form. Let’s change 0.9 to a percent. Move the decimal point two places to the right and add the percent sign.

Now, compare 18% and 90%.

18% is less than 90%.

Write 0.56, 34%,

, and in order from least to greatest.First, rewrite them in the same form. Let’s convert all of them to percents. 34% is already in percent form.

Convert 0.56 to a percent. Move the decimal point two places to the right and add the percent sign.

Next, find the equivalent fractions of \begin{align*}\frac{9}{10}\end{align*} and as fractions over 100 and convert them to percents. Multiply the numerator and denominator of by 10. Multiply the numerator and denominator of by 50.

Then, compare the percents.

Finally, write them in the order from least to greatest.

### Examples

#### Example 1

Earlier, you were given a problem about Steve and Nickie and their bet.

Steve has read

of the book and Nickie has read 65% of the book. To find out who has read the farthest, compare the quantities.First, rewrite

as a percent. Find the equivalent fraction of as a fraction over 100 and convert to a percent. Multiply the numerator and denominator by 20.

Next, compare the percents.

60% is less than 35%. Nickie is farther along than Steve and will get to decide on lunch.

#### Example 2

Write the values in order from least to greatest.

\begin{align*}\frac{83}{100} , 0.16, 33\%, \frac{4}{5}\end{align*}

First, rewrite then in the same form. Let’s write them as decimals. 0.16 is already in decimal form.

Convert

and to decimals. The fraction is 83 out of 100 or 83 hundredths. Convert to a decimal by dividing 4 by 5.

Next, convert 33% to a decimal. Move the decimal point two places to the left and remove the percent sign.

Then, compare the decimals.

Finally, write them in the order from least to greatest.

#### Example 3

Compare the values.

First, rewrite them in the same form. Convert 19% to a decimal. Move the decimal two places to the left and remove the percent sign.

Next, compare the decimals.

0.19 and 19% are equal values.

#### Example 4

Compare the values.

First, rewrite them in the same form. Let’s convert both

and 45% to decimals. Divide 2 by 5.

Move the decimal place two places to the left and remove the percent sign.

Next, compare the decimals.

is less than 45%.

#### Example 5

Compare the values.

First, these values are in the same form. Compare the two percents.

56% is greater than 21%.

### Review

Write the following values in order from least to greatest.

- \begin{align*}\frac{16}{100}, .27, 53\%, \frac{1}{5}\end{align*}
- \begin{align*}\frac{99}{100}, .30, 68\%, \frac{9}{10}\end{align*}
- \begin{align*}\frac{18}{100}, .99, 87\%, \frac{10}{20}\end{align*}
- \begin{align*}\frac{88}{100}, .18, 23\%, \frac{1}{5}\end{align*}
- \begin{align*}\frac{93}{100}, .98,6\%, \frac{1}{2}\end{align*}
- \begin{align*}\frac{77}{100}, .37,93\%, \frac{2}{5}\end{align*}
- \begin{align*}\frac{12}{100}, .76,13\%, \frac{1}{3}\end{align*}
- \begin{align*}\frac{9}{100}, .2, 67\%, \frac{4}{5}\end{align*}
- \begin{align*}\frac{88}{100}, .29, 35\%, \frac{2}{10}\end{align*}

Compare the following values using <, > or =.

- \begin{align*}\frac{6}{7}\end{align*} and 35%
- \begin{align*}\frac{3}{4}\end{align*} and 75%

### Review (Answers)

To see the Review answers, open this PDF file and look for section 8.16.